Faculty Advisor
Chris Velissaris
Keywords
Physics-informed neural networks, Helmholtz equation, computational electromagnetics, SIREN, multiphysics modeling, Convolutional neural networks, OpenCLIP, ResNet-18
Abstract
Physics-informed neural networks solve the Helmholtz equation without labeled data, but a low residual alone does not confirm that a solution preserves the physical distinction a downstream task depends on. We trained a four-layer SIREN with physics-based residuals, a Sommerfeld condition, Adam, and L-BFGS, modeling a Gaussian source and a plane wave scattering from a small dielectric inclusion. Fine-tuning from four base models produced 600 complex fields spanning omega = 4 to 20. A compact CNN, three ResNet-18 variants, and a frozen OpenCLIP encoder classified these fields under five random seeds. The CNN achieved (95.65 +/- 0.77)% accuracy, outperforming OpenCLIP at (79.35 +/- 5.04)%, fine-tuned ResNet-18 at (73.48 +/- 5.47)%, the linear probe at (70.22 +/- 7.15)%, and ResNet-18 from scratch at (54.35 +/- 4.35)%; Cohen's d ranged from 4.5 to 13.2. The CNN's only systematic error occurred in the free-space class at high frequency, confused with the dielectric case, and did not track residual magnitude: the affected class had the lowest residual of the four. A convergence study at omega = 19.5 found the field had not stabilized under the original budget: longer training left the residual an order of magnitude above convergence while the free-space to dielectric separation converged to a value roughly 37% larger than the dataset's. Natural-image features transferred poorly to these fields. Residual, field stability, and the distinction a classifier depends on are separate diagnostics that do not track one another; classification exposed a degradation that residual and visual inspection alone did not.
Rights
This work is licensed under a Creative Commons Attribution 4.0 International License.
College
College of Sciences
STARS Citation
Taylan, Bryan; Corzo, Patrick; Velissaris, Chris; and Panagiotakopoulos, Theodoros, "Studying Electromagnetic Wave Scattering from Small Dielectric Particles Using Neural Networks" (2026). Undergraduate Scholarship and Creative Works. 11.
https://stars.library.ucf.edu/undergradscholar/11